My friend runs through her allowed data (limited data plan) quickly. Could it be that despite not opening her email, she is using data merely by having data turned on?
The best way to check data usage is via Settings, Mobile Data, where there is a breakdown of app data usage. Also in there, you can set a mobile data usage warning and limit, so that you don't exceed your allowance.
There are things you can do to reduce data use....if your friend still has problems or needs further advice, please get back to us.
I didn't see where you mentioned WiFi use. Does this person have access to WiFi at all? I share 2 GB of Verizon data per month with two more family members and we seldom go over 1.5 per month. We have WiFi at home, work and can quickly jump into places that have free WiFi.
If this isn't possible, you might want to have her increase her plan to include more data.